Are skyscrapers the tallest constructions in a city?

Answer 1

A skyscraper is a tall, continuously habitable building of many stories, usually designed for office and commercial use (usually having a steel framework from which curtain walls are suspended, rather than load-bearing walls of conventional construction). Thus, yes "skyscrapers" would normally be the tallest constructions in a city.

However, in a city where there is no high rise, modern construction, the tallest building would not be called a skyscraper.